Non-Abelian statistics of vortices with non-Abelian Dirac fermions

Abstract

We extend our previous analysis on the exchange statistics of vortices having a single Dirac fermion trapped in each core, to the case where vortices trap two Dirac fermions with U(2) symmetry. Such a system of vortices with non-Abelian Dirac fermions appears in color superconductors at extremely high densities, and in supersymmetric QCD. We show that the exchange of two vortices having doublet Dirac fermions in each core is expressed by non-Abelian representations of a braid group, which is explicitly verified in the matrix representation of the exchange operators when the number of vortices is up to four. We find that the result contains the matrices previously obtained for the vortices with a single Dirac fermion in each core as a special case. The whole braid group does not immediately imply non-Abelian statistics of identical particles because it also contains exchanges between vortices with different numbers of Dirac fermions. However, we find that it does contain, as its subgroup, a genuine non-Abelian statistics for the exchange of the identical particles, that is, vortices with the same number of Dirac fermions. This result is surprising compared with conventional understanding because all Dirac fermions are defined locally at each vortex, unlike the case of Majorana fermions for which Dirac fermions are defined non-locally by Majorana fermions located at two spatially separated vortices.

32 pages, no figures, v3: published version

References in corpus (20)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Color superconductivity in dense quark matter
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Instabilities of Non-Abelian Vortices in Dense QCD
• Color Magnetic Flux Tubes in Dense QCD
• Color Magnetic Flux Tubes in Dense QCD. II: Effective World-Sheet Theory
• Weak topological insulator with protected gapless helical states
• Topological Majorana and Dirac zero modes in superconducting vortex cores
• Fermion structure of non-Abelian vortices in high density QCD
• Confined Monopoles Induced by Quantum Effects in Dense QCD
• Index theorem and Majorana zero modes along a non-Abelian vortex in a color superconductor
• Majorana meets Coxeter: Non-Abelian Majorana Fermions and Non-Abelian Statistics
• Topological Interactions of Non-Abelian Vortices with Quasi-Particles in High Density QCD
• Dirac returns: non-Abelian statistics of vortices with Dirac fermions
• Non-Abelian statistics of vortices with multiple Majorana fermions
• Zero Energy Modes and Statistics of Vortices in Spinful Chiral p-Wave Superfluids
• Singular and Half-Quantum Vortices and Associated Majorana Particles in Superfluid 3He-A between Parallel Plates

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• The effective action of a BPS Alice string
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Quark-Hadron Crossover with Vortices
• Twisted-Mass Potential on the Non-Abelian String World Sheet Induced by Bulk Masses
• Shot noise signatures identifying non-Abelian properties of Jackiw-Rebbi zero modes